A double-headed piston type swash plate compressor includes a rotation shaft, a housing, a swash plate, two cylinder bores, a double-headed piston, and two shoes. The double-headed piston includes two shoe holders, a neck, two heads, and two coupling portions. Each of the coupling portions includes an outer portion and an inner portion. A direction orthogonal to both of an opposing direction of the inner portion and the outer portion and the axial direction of the double-headed piston is referred to as a widthwise direction. The neck is larger in the widthwise direction than in the opposing direction so that the neck is deformable in the opposing direction. Each of the two coupling portions has a width that is less than or equal to a width of the neck. The inner portion includes a narrow portion. The narrow portion is at least partially located closer to the head than the shoe holder in the inner portion. The two coupling portions are deformable in the widthwise direction when the swash plate applies load to the double-headed piston.